Fault structure reconstruction is an important aspect of magnetic prospecting as it contributes to understanding tectonic history, hazard assessment, and infrastructure planning. Metaheuristics have proven useful in estimating fault structure parameters from geophysical anomalies. Recently, a modified version of the Backtracking Search Optimization Algorithm (BSA), named mBSA, has been proposed that combines mutation steps of BSA and Differential Evolution (DE) algorithms to achieve a better balance between exploration and exploitation. Here, we present imBSA as an efficient approach that builds on the improvements of mBSA. It uses an adaptive amplitude control factor in the mutation step derived from a normally distributed random number obtained via an exponential function. The performances of these approaches were tested on some widely used benchmark functions such as Rosenbrock, Rastrigin, Griewank, and Himmelblau. Synthetic magnetic fault anomalies were evaluated with and without noise, as well as three real anomalies from the Dehri (India), Perth Basin, and Lachlan Fold Belt (Australia). Prior to the optimizations, the solvability of the model parameters was examined using some error topography images. The obtained solutions in the synthetic cases were evaluated using principal component analysis. In addition, a novel visualization option for high-dimensional optimization problems was introduced. The experiments showed that imBSA has a faster convergence rate and better optimization statistics compared to BSA and mBSA. Therefore, it is believed to be an efficient and good alternative tool to widely used metaheuristics such as Particle Swarm Optimization and DE in explaining geophysical anomalies and optimization problems in other geoscientific disciplines.